I linked a good resource that explains what you asked below.
This is impossible to prove, as the square root of 2 is irrational.
No; you can prove the square root of any positive number that's not a perfect square is irrational, using a similar method to showing the square root of 2 is irrational.
The square root of 2 is an irrational number
The square root of 3 is an irrational number
No. For example, -root(2) + root(2) is zero, which is rational.Note that MOST calculations involving irrational numbers give you an irrational number, but there are a few exceptions.
The square root of 2 is 1.141..... is an irrational number
This is impossible to prove, as the square root of 2 is irrational.
It is known that the square root of an integer is either an integer or irrational. If we square root2 root3 we get 6. The square root of 6 is irrational. Therefore, root2 root3 is irrational.
No; you can prove the square root of any positive number that's not a perfect square is irrational, using a similar method to showing the square root of 2 is irrational.
Yes, the square root of 2 is an irrational number.
Yes. The square root of a positive integer can ONLY be either:* An integer (in this case, it isn't), OR * An irrational number. The proof is basically the same as the proof used in high school algebra, to prove that the square root of 2 is irrational.
The square root of 2 is an irrational number
2 is a prime number and its square root is an irrational number that cannot be expressed as a fraction
irrational
No, the square root of an irrational number is not always rational. In fact, the square root of an irrational number is typically also irrational. For example, the square root of 2, which is an irrational number, is itself irrational. However, there are exceptions, such as the square root of a perfect square of an irrational number, which can be rational.
Yes. For example, the square root of 3 (an irrational number) times the square root of 2(an irrational number) gets you the square root of 6(an irrational number)
Yes, they are irrational.